Setting
Let denote a random vector (corresponding to the measurements), taken from a parametrized family of probability density functions or probability mass functions, which depends on the unknown deterministic parameter . The parameter space is partitioned into two disjoint sets and . Let denote the hypothesis that, and let denote the hypothesis that . The binary test of hypotheses is performed using a test function .
meaning that is in force if the measurement and that is in force if the measurement . Note that is a disjoint covering of the measurement space.
Read more about this topic: Uniformly Most Powerful Test
Famous quotes containing the word setting:
“We don’t arrive at it by standing on one leg or on the first day of our setting out—but though we may jostle one another on the way that is no reason why we should strike or trample—elbowing’s enough.”
—George Gordon Noel Byron (1788–1824)
“With wonderful art he grinds into paint for his picture all his moods and experiences, so that all his forces may be brought to the encounter. Apparently writing without a particular design or responsibility, setting down his soliloquies from time to time, taking advantage of all his humors, when at length the hour comes to declare himself, he puts down in plain English, without quotation marks, what he, Thomas Carlyle, is ready to defend in the face of the world.”
—Henry David Thoreau (1817–1862)
“Dandyism is the last flicker of heroism in decadent ages.... Dandyism is a setting sun; like the declining star, it is magnificent, without heat and full of melancholy. But alas! the rising tide of democracy, which spreads everywhere and reduces everything to the same level, is daily carrying away these last champions of human pride, and submerging, in the waters of oblivion, the last traces of these remarkable myrmidons.”
—Charles Baudelaire (1821–1867)